A source close to President Sergio Mattarella, who vetoed Savona as finance minister and appointed Cottarelli to form a government to oversee fresh elections around the end of the year, said the two men had "decided together not to rush things, (to favor) a possible political government".
"I have given up my mandate to form the government of change", said lawyer and political novice Giuseppe Conte, 53, plunging the country into a political crisis almost three months after March's inconclusive general election.
The leaders of two populist parties, Italy's anti-migrant League party and the anti-establishment 5-Star Movement, earlier announced they had reached a deal that would enable them to form a government.
As market tensions eased following Tuesday's panic, Mattarella held another round of informal talks in Rome with Cottarelli and then Five Star leader Luigi Di Maio.
Paolo Savona, whose nomination sparked a constitutional crisis, would still join the cabinet, but as European affairs - not finance - minister.
Mr Mattarella will have to agree to the proposed coalition and cabinet.
Cottarelli meanwhile has a caretaker team ready to step in should the Five Star-League negotiations fail - but the lineup is doomed to lose a confidence vote in the populist-dominated parliament, meaning that elections would likely be held after August.
However, League leader Matteo Salvini, who is surging in opinion polls, appeared to throw cold water on the notion that his party and 5-Star could try again to take power, saying Italy should return to an election as soon as possible.
Giuseppe Conte had left Rome on Sunday, relinquishing his brief role as premier-designate, after Mr Mattarella rejected the populist parties' Cabinet list. None of the parties obtained the majority required to form the government.
Cottarelli said it had been a "great honour to work for the country, if only for a short time" and that a political government was "a better solution".
The League leader is advocating for an election at the earliest possible date, which is no surprise since polls suggest his party would be the biggest victor if the Italians return to the polls.
That election, expected in the autumn or early next year, is shaping up to be a battle over Italy's future in Europe.
Prime Minister-designate Carlo Cottarelli and President Sergio Mattarella met this morning, as the country lumbers on without a government in place. The former even called for Mattarella's impeachment, but withdrew that threat after only a few days. Di Maio has claimed repeatedly that he does not intend to lead Italy out of the Euro, notwithstanding the fact that this was an MS5 official policy for years.
Luigi Di Maio of the anti-establishment Five Star Movement and Matteo Salvini of the anti-immigrant League said they will propose law professor Giuseppe Conte, 53, who has no political experience, as prime minister.
The President and Prime Minister-designate, however, have chose to maintain the current situation and not rush things out until there's a possibility of holding a fresh election to form a government by the end of the year.
Elections could benefit Salvini, however, as recent polling by IndexResearch put the League at 22%, five points up from its vote share in the March 4 ballot. "But I no longer accept that everything which is going wrong in South of Italy, in Mezzogiorno, is explained by the fact that the EU or the European Commission would not do enough", he said after leaving a meeting in Brussels.